US7271395B2 - Device and method for the measurement of depth of interaction using co-planar electrodes - Google Patents
Device and method for the measurement of depth of interaction using co-planar electrodes Download PDFInfo
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- US7271395B2 US7271395B2 US11/174,241 US17424105A US7271395B2 US 7271395 B2 US7271395 B2 US 7271395B2 US 17424105 A US17424105 A US 17424105A US 7271395 B2 US7271395 B2 US 7271395B2
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01T—MEASUREMENT OF NUCLEAR OR X-RADIATION
- G01T1/00—Measuring X-radiation, gamma radiation, corpuscular radiation, or cosmic radiation
- G01T1/16—Measuring radiation intensity
- G01T1/17—Circuit arrangements not adapted to a particular type of detector
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01T—MEASUREMENT OF NUCLEAR OR X-RADIATION
- G01T1/00—Measuring X-radiation, gamma radiation, corpuscular radiation, or cosmic radiation
- G01T1/16—Measuring radiation intensity
- G01T1/24—Measuring radiation intensity with semiconductor detectors
- G01T1/247—Detector read-out circuitry
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- the present invention relates to high-resolution co-planar grid sensors for gamma-ray detection, and more particularly, to a method and device for measuring the depth of interaction in co-planar grid sensors to increase resolution of detection.
- Compound semiconductor sensors like the ones based on cadmium zinc telluride (CdZnTe) material, for example, are being considered in an increasing number of room-temperature gamma-ray detection applications. Though more convenient and practical when used at room-temperature, these sensors suffer a loss of signal to noise compared to conventionally cooled sensors.
- cadmium zinc telluride (CdZnTe) material for example, are being considered in an increasing number of room-temperature gamma-ray detection applications. Though more convenient and practical when used at room-temperature, these sensors suffer a loss of signal to noise compared to conventionally cooled sensors.
- Several solutions have been proposed and some successfully adopted in order to compensate for the resulting substantial collection deficiency.
- the charges, both electrons and holes, generated by the ionizing gamma radiation are subject to substantial trapping effects.
- the holes are limited by a much shorter trapping length compared to the electrons; therefore, their contribution to the induction of charge on the electrodes is negligible and subsequently, the induction depends strongly on the electrons.
- This dependence on the electrons makes the signals induced on the electrodes strongly dependent on the depth of the ionizing interaction, leading to relevant degradation of spectral signal resolution. Therefore, there is a need for an electrode configuration that makes a device that is sensitive to one kind of charge only, but with a resolution that is independent of the depth of the interaction.
- a CPG 10 includes a cathode 12 , and an anode side 14 .
- the anode side 14 includes two co-planar interdigitally connected grids in place of the conventional single electrode.
- One of the grids is a collecting grid 16 and the other is a non-collecting grid 18 .
- a small bias voltage is applied across the collecting 16 and non-collecting grid 18 so that all the electrons in proximity of the grids are collected substantially only by the collecting grid 16 .
- a high voltage supply supplies a high voltage to the cathode electrode 12 , thus generating an electric field in the bulk of the compound semiconductor 23 .
- the depth of interaction refers to a distance of an event from the anode side 14 . Therefore, a deep-interacting event 32 is characterized as an ionizing event occurring close to the cathode 12 , while a non-deep-interacting event 34 is characterized as an ionizing event close to the grids 14 .
- the conventional CPG sensor is still limited by the trapping of the electrons in the bulk.
- the effect of trapping is shown with solid lines 36 in the signals of FIG. 1 , and can be compared to the ideal case of no trapping effects shown with dotted lines 38 .
- the conventional CPG sensor does not compensate for the residual deficit in pulse height due to the residual trapping effect on the electrons.
- the relative gain compensation technique includes lowering the gain of the non-collecting grid below unity relative to that of the collecting grid.
- the other method referred to as a cathode amplitude signal technique includes keeping the gain at unity and weighting each event by measuring its depth of interaction through measurement of the amplitude of the cathode signals.
- the relative gain compensation technique essentially re-introduces a small amount of induction from the electrons traveling in the bulk back into the sensor system.
- the amplitude of the deep-interacting events is increased, while the one of the non-deep-interacting events is reduced, resulting in a first order compensation of the trapping effects.
- the optimum value of the relative gain typically ranges between 0.6 and 0.9, depending on the quality of the sensor, on the bias voltage and on the temperature.
- the gain is normally set by modifying the value of a passive element in the differential amplifier, i.e., a resistor.
- the relative gain compensation technique advantageously does not require complex electronics, the correction is roughly linear, providing only a first order compensation for the trapping effects. As a result, the method is limited to a small amount of achievable compensation and thus the sensor resolution is minimally improved.
- a second disadvantage is that, if the relative gain needs to be modified, for example, due to replacement of the sensor or a change in voltage and/or temperature, a hardware change is needed, which is impractical especially for commercial applications.
- the cathode amplitude signals technique consists of measuring, along with the amplitude of the difference signal, the amplitude of the cathode signal. By calculating the ratio between the difference and the cathode amplitudes, it is possible to extract the depth of the interaction of the event.
- the difference signal of the event can be corrected (weighted) for the trapping effect according to the value of the associated depth of interaction.
- the optimum weighting parameters depend on the quality of the sensor, on the bias voltage and on the temperature.
- This technique allows a higher order compensation of the trapping effects, thus achieving a better resolution when compared to the previous technique.
- a second advantage is that the optimization can be performed via software, with straightforward practical consequences.
- more complex electronics are disadvantageously required, including an additional front-end channel for processing the cathode signal, as well as large and bulky high voltage capacitors for coupling the high voltage cathode to the front-end electronics.
- the present invention which addresses the needs of the prior art, relates to an efficient method and device for measuring the depth of interaction in co-planar electrode sensors such as a co-planar grid sensor (CPG) to increase resolution of detection without the addition of complex and bulky electronics. Therefore, the present invention also provides an efficient high spectral resolution device for use in detecting ionizing radiation, which may be used at room-temperature.
- co-planar electrode sensors such as a co-planar grid sensor (CPG) to increase resolution of detection without the addition of complex and bulky electronics. Therefore, the present invention also provides an efficient high spectral resolution device for use in detecting ionizing radiation, which may be used at room-temperature.
- CPG co-planar grid sensor
- a method of the present invention for measuring a depth of interaction of an ionizing event using a co-planar collecting electrode and a non-collecting electrode includes obtaining a difference in time between a time of detection (or arrival) of a charge generated by the event at the collecting electrode and a time of occurrence of the event, as detected by the collecting or non-collecting electrode; and calculating the depth of interaction from the difference in time.
- the method may be adapted to provide a high-resolution ionizing radiation sensor, where the method further includes weighting a difference signal, obtained by measuring a difference between the collecting and non-collecting electrode signal, by the depth of interaction to improve a spectral resolution of detection of the ionizing event.
- a device of the present invention for measuring a depth of interaction of an ionizing event, using a co-planar anode electrode sensor including a coplanar non-collecting electrode and a collecting electrode includes a first channel for inputting a collecting electrode signal from a collecting electrode, and a second channel for inputting a non-collecting electrode signal from a non-collecting electrode.
- the collecting electrode signal includes an event pulse including an event leading edge occurring at a time of occurrence of an ionizing event.
- the device further includes a differential amplifier operatively connected to the first channel and the second channel. An output from the differential amplifier provides a difference signal between the non-collecting electrode signal and the collecting electrode signal.
- the difference signal includes a difference pulse having a leading edge occurring at a time of detection of a charge generated in response to the ionizing event.
- the device additionally includes a first comparator operatively connected to the collecting electrode and a first threshold control, which provides a first threshold reference level adjusted to correspond to the event leading edge. The first comparator outputs a first time at which the collecting electrode signal crosses the first threshold reference level, where the first time corresponds to the time of occurrence.
- a second comparator in the device is operatively connected to the output of the differential amplifier and a second threshold reference level adjusted to correspond to the leading edge of the difference pulse.
- the second comparator outputs a second time at which the difference signal crosses the second threshold reference level, where the second time corresponds to the time of detection.
- the device may be integrated into an Application Specific Integrated Circuit.
- the device may also include a processor for calculating a timing difference, wherein the timing difference equals the second time minus the first time, and for calculating the depth of interaction of the ionizing event from the timing difference, wherein the processor further weights the difference signal by the calculated depth of interaction to improve a spectral resolution of the co-planar anode electrode sensor.
- the present invention also includes a high-resolution ionizing detector device including a combination of a co-planar anode electrode sensor, and a device for measuring a depth of interaction of an ionizing event using the co-planar anode electrode sensor.
- the sensor includes a non-collecting anode electrode, a collecting anode electrode, a cathode, and a substrate, where an ionizing event occurs at a depth of interaction in the substrate.
- the non-collecting anode electrode and the collecting anode electrode are co-planar, and a charge generated by the ionizing event is collected at the collecting anode electrode.
- the device of the combination includes a first channel for inputting a collecting electrode signal from the collecting electrode, and a second channel for inputting a non-collecting electrode signal from the non-collecting electrode.
- the collecting electrode signal includes an event pulse including an event leading edge occurring at a time of occurrence of an ionizing event.
- the device of the combination further includes a differential amplifier operatively connected to the first channel and the second channel.
- An output from the differential amplifier provides a difference signal between the non-collecting electrode signal and the collecting electrode signal.
- the difference signal includes a difference pulse having a leading edge occurring at a time of detection of a charge generated in response to the ionizing event.
- the device additionally includes a first comparator operatively connected to the collecting electrode and a first threshold control, which provides a first threshold reference level adjusted to correspond to the event leading edge. The first comparator outputs a first time at which the collecting electrode signal crosses the first threshold reference level, where the first time corresponds to the time of occurrence.
- a second comparator in the device is operatively connected to the output of the differential amplifier and a second threshold reference level adjusted to correspond to the leading edge of the difference pulse.
- the second comparator outputs a second time at which the difference signal crosses the second threshold reference level, where the second time corresponds to the time of detection.
- the collecting electrode of the sensor may be a collecting grid and the non-collecting electrode a non-collecting grid in a co-planar grid (CPG) sensor, which provides the input signals to the channels of the device.
- CPG co-planar grid
- the device may be used to produce a high-resolution co-planar grid sensor operating at room temperature for the detection of, for example, gamma ray events.
- the substrate of the sensor may be a semiconductor.
- useful semiconductors include Cadmium Zinc Telluride, Cadmium Telluride and Mercuric Iodide.
- FIG. 1 is a schematic of a conventional prior art co-planar grids (CPG) sensor.
- CPG co-planar grids
- FIG. 2 is an embodiment of a device of the present invention for measuring depth of interaction from a CPG sensor.
- FIG. 3A is a plot of results of an experiment for detection of an ionizing event close to the cathode of a CPG sensor using the device of FIG. 2 .
- FIG. 3B is a plot of results of an experiment for detection of an ionizing event close to the grids of a CPG sensor using the device of FIG. 2 .
- FIG. 4 is an electrical schematic representation of an embodiment of an ASIC of the present invention for measuring depth of interaction from a CPG sensor.
- FIG. 5 is a plot of an uncompensated spectrum of a known Cesium (Cs) standard, 137 Cs, using only the CPG shown in FIG. 4 .
- FIG. 6 is a plot of a measured spectrum of the 137 Cs standard using the ASIC shown in FIG. 4 , to apply the prior art relative gain compensation technique, which includes lowering the gain of the non-collecting grid below unity relative to that of the collecting grid.
- FIG. 7 is a plot of a measured spectrum of the 137 Cs standard using the ASIC shown in FIG. 4 , to apply the prior art the cathode/difference ratio technique.
- FIG. 8 is a plot of a measured spectrum of the 137 Cs standard using the ASIC shown in FIG. 4 , to apply the method of the present invention.
- FIG. 9 is a bi-parametric spectrum of measurements of the 137 Cs standard for different depths of interaction using the ASIC of FIG. 4 and applying the method of the present invention.
- the present invention provides an efficient method and device for measuring the depth of interaction of ionizing radiation in co-planar electrode sensors, in particular, co-planar grid sensors, to increase resolution of detection.
- an efficient high spectral resolution device for detecting ionizing radiation at room temperature is provided.
- the present invention provides a method and device for measuring a depth of interaction of an ionizing radiation (e.g., gamma ray, x-ray, or neutron) event by using timing information from co-planar anode electrode signals only.
- an ionizing radiation e.g., gamma ray, x-ray, or neutron
- Any co-planar electrode configuration which includes at least one collecting anode and one non-collecting anode of suitable shape and dimension as known to those skilled in the art, may be used to provide the collecting and non-collecting signals.
- the collecting anode is a collecting grid and the non-collecting electrode is a non-collecting grid.
- Each grid includes multiple electrode fingers. The collecting grid fingers are interleaved with the non-collecting grid fingers, forming multiple adjacent pairs of co-planar non-collecting/collecting anode surfaces.
- the method includes obtaining a difference signal 30 between a non-collecting grid 18 and a collecting grid 16 .
- a difference in time i.e., a timing difference
- the timing difference corresponds to the depth of interaction.
- the difference signal 30 corresponding to the ionizing event can then be corrected (weighted) for the trapping effect according to the value of the associated depth of interaction.
- the difference in time may also be measured between a leading edge of a non-collecting grid signal and the difference signal 30 using the method of the present invention.
- the depth of interaction may be advantageously calculated using only one collecting electrode and one non-collecting electrode, which are co-planar.
- FIG. 2 One embodiment of a device 40 of the present invention for providing a measurement of the depth of interaction is shown in FIG. 2 .
- the device 40 provides two channels for inputting the collecting grid signal 26 and the non-collecting grid signal 28 .
- the device 40 may include various front-end electronics, including charge amplifiers 41 to process the raw grid signals 26 and 28 .
- an ionizing event generates a pulse signal corresponding to each of the collecting grid 26 and the non-collecting grid 28 , where a leading edge of each pulse corresponds to the time of occurrence of the event 22 t c .
- the two signals 26 and 28 are identical until the charge generated by the event is very close to the grids. At some trivial distance from the grids, the charge is pulled toward the collecting grid 16 , so that immediately after a time of detection 24 t d , the signals differ.
- the device 40 of the present invention includes a differential amplifier 42 to provide the difference signal 30 between these input signals 26 and 28 by operatively connecting the collecting grid 16 and the non-collecting grid 18 to the differential amplifier 42 .
- the collecting grid 16 is also operatively connected to a first comparator 44 .
- the first comparator 44 in cooperation with a threshold control 47 to provide a first threshold reference level, uses the collecting grid signal 26 to measure a first time t c 22 corresponding to a time of occurrence of the ionizing event occurring at some depth inside the substrate 23 relative to the grid 16 .
- An output of the differential amplifier 42 is operatively connected to a second comparator 46 .
- the second comparator 46 measures a second time t d 24 corresponding to a time of detection of the charge occurring once it is very near the grid 16 .
- the second time 24 is measured from the difference signal 30 , in cooperation with a threshold control 48 to provide a second threshold reference level as input to the second comparator 46 .
- the threshold control levels to each comparator 47 and 48 are adjusted, as is well-known to those skilled in the art, to provide a zero or other threshold crossing of the collecting grid signal 26 and the difference signal 30 .
- the first threshold reference level and the second reference level may be the same and simultaneously adjustable, or may be provided as separate inputs.
- a measure of time of occurrence t c 22 of the event at some depth or distance from the grid 16 is provided by the first timing signal 50 at the output of the first comparator 44 .
- a measure of time t d 24 corresponding to the charge at the grid 16 is then provided by the second timing signal 52 output from the second comparator 46 .
- the timing difference t d ⁇ t c between the first timing signal 50 and the second timing signal corresponds to the depth of interaction.
- the non-collecting grid signal 28 is used in the place of the collecting grid signal 26 to the comparator 44 and a first threshold crossing measured according to means known to those skilled in the art to provide the time of occurrence t c 22 .
- the associated timing difference t d ⁇ t c is large, while in the case of the non-deep-interacting events 34 close to the grids the timing difference is small. Therefore, a high resolution is achieved according to a method and device 40 of the present invention without the associated disadvantages of additional electronic channel and bulk coupling capacitors characteristic of the prior art.
- a high-resolution co-planar grid sensor device of the present invention therefore, includes a combination of the device 40 and a CPG sensor 51 including the collecting grid 16 and the non-collecting grid 18 .
- experimental results 60 using the circuit 40 with a CPG sensor is provided for interactions close to the cathode, i.e., deep-interacting events.
- a timing difference, t d ⁇ t c 49 on the order of hundreds of nanoseconds can be observed.
- the first timing signal 50 (time of occurrence) and the second timing signal (time of detection) 52 were obtained by inputting the collecting grid 26 and non-collecting grid signals 28 into the differential amplifier 42 , preferably after processing by front-end electronics including the charge amplifiers 41 to obtain the difference signal 30 .
- FIG. 3B provides experimental data 70 for interactions close to the grids. In this case, which corresponds to non-deep-interacting events, a negligible timing difference 72 is observed.
- the CPG device of the present invention provides a compact and efficient solution for large-volume room-temperature ionizing radiation sensors, such as Gamma-ray detectors and spectrometers.
- the device is particularly useful for applications ranging from nuclear material safeguard to radioisotope identification in security and defense, environmental remediation, well logging, medical diagnostics, and gamma-ray astronomy.
- the present invention includes a compact, efficient Application Specific Integrated Circuit (ASIC) that replaces discrete components including those in the device 40 to provide a measurement of the depth of interaction in a compact, efficient package.
- ASIC Application Specific Integrated Circuit
- an ASIC 80 of the present invention provides amplification of grid signals, the difference signal, and the first t c and second t d timing signals.
- the ASIC also includes adjustable relative gain and high order filtering.
- the ASIC 80 may also provide a measurement of the cathode signal.
- the ASIC 80 provides high sensitivity measurements by making use of the timing signals from the grid according to the present invention.
- the ASIC 80 can provide the capability to measure all signals of interest and provide electron trapping compensation according to previous techniques, such as the relative gain technique and cathode measurement technique discussed above.
- At least two front-end channels are provided, one 82 for the collecting grid signal, and one 84 for the non-collecting grid signal.
- An additional channel 86 may also be included for the cathode signal.
- Each channel of the ASIC may include a test capacitor, preferably of about 500 fF, for external enablement through a dedicated switch (not shown).
- gain can be switched, for example, between 36 mV/fC and 18 mV/fC, in order to cover an energy range up to at least 3 MeV.
- the total dissipated power of an ASIC according to the present invention is preferably 25 mW or less from a single voltage supply, e.g., a +2.5V supply.
- the ASIC incorporates 0.25 ⁇ m technology, which may be provided, for example, by the Taiwan Semiconductor Manufacturing Company, 8 Li-Hsin Rd. VI, Hsinchu Science Park, Hsinchu, Taiwan 300-77, R.O.C. Dimensions of the ASIC are preferably 3.5 ⁇ 3.5 mm 2 or less.
- Front-end stages 88 are preferably provided with a p-channel input device. Noise analysis and experimentation have demonstrated that due to the correlation associated with the inter-grid capacitance, the series input noise from the front-end can severely limit the resolution of this type of system. The series noise, dominated by the low-frequency component, was found to be 4-5 times lower using the p-channel device.
- the front-end electronics 88 include a low-noise p-channel charge amplifier (CA) 90 , which is based on a dual-stage charge gain configuration to operatively connect each channel 82 and 84 to a differential amplifier (DA) 92 .
- the differential amplifier 92 is designed, for example, to provide a relative gain of at least from about 0.4 to about 1.5, according to methods known to those skilled in the art.
- Additional front-end electronics may also be included after each CA 90 to generate a first pole of a shaping amplifier 94 , also referred to herein as a shaper 94 , which filters and shapes the pulse signal output from the DA 92 .
- a shaping amplifier 94 also referred to herein as a shaper 94 , which filters and shapes the pulse signal output from the DA 92 .
- the shaper 94 is preferably a 5th order with complex conjugate poles and band-gap referenced baseline stabilizer [BLH] 95 .
- a band-gap reference 93 stabilizes the baseline of the pulses for both shapers 94 and 104 .
- the peaking time of the shaping amplifier (“shaper”) 94 is appropriately chosen for the particular application, as those skilled in the art will appreciate. In one embodiment, the peaking time is selectable between about 1.2 ⁇ s and 2.4 ⁇ s. Consequently, the ASIC 80 is suitable for use even with CPG sensors affected by higher leakage currents (i.e. higher shot noise).
- Buffers may also be provided (not shown) to make available to dedicated outputs: the unshaped signals after the first pole 96 , the amplified collecting grid signal 98 and non-collecting grid signal 100 , and their difference 102 .
- a similar shaping amplifier 104 is optionally provided to process the event pulse signal 86 input from the cathode.
- the ASIC 80 thus provides other options for compensating event data for depth of interaction according to prior art techniques using the cathode signal, measuring the timing of the collecting signal is preferable to measuring the cathode signal, as discussed above.
- the ASIC includes a first comparator 106 and second comparator 108 with a first threshold control 110 and a second threshold control 111 respectively.
- a measure of the first time t c 22 (time of occurrence) is provided by a first timing signal 112 output from the first comparator 106 and a second time t d 24 (time of detection) is provided by a second timing signal 114 output from the second comparator 108 .
- the threshold control reference level to each comparator is adjusted and set, as is well-known to those skilled in the art, to provide a zero or other threshold crossing of the collecting grid signal 82 and the difference signal 102 at the respective outputs of the comparators.
- the timing difference t d ⁇ t c between the collecting signal and the difference signal as measured at the output of the comparators is a measure of the depth of interaction and advantageously requires only the grid signals (collecting and difference) as input.
- the bi-parametric result is then used to compensate for the electron trapping. Therefore, no hardware adjustments are required to the CPG sensor and the technique can be applied during the acquisition via software.
- the method and device of the present invention does not require the additional cathode amplification and processing required for cathode measurement techniques, offering advantages in terms of power and area, especially by avoiding the need for bulky capacitors and resistors to couple the high-voltage cathode to the front-end.
- a high-resolution ionizing detection device includes either an embodiment of the device 40 having discrete components or an ASIC, such as the ASIC 80 of FIG. 4 , which integrates the discrete components, in combination with a co-planar electrode sensor for detecting an ionizing event.
- the co-planar sensor preferably includes a collecting grid and a non-collecting grid, as well as a substrate and cathode. Preferably, electrons are detected, and the sensor is operated at room temperature.
- the substrate includes any material capable of detecting an ionizing event.
- the substrate includes a semiconductor.
- Examples of semiconductors for use in the sensor include Cadmium Zinc Telluride, Cadmium Telluride and Mercuric Iodide.
- FIG. 4 and FIGS. 5-8 experimental measurements of an energy spectrum of a known Cesium (Cs) standard, 137 Cs, were performed using the ASIC 80 of the present invention coupled to a CPG sensor 116 .
- an uncompensated spectrum 120 for the 137 Cs standard was first recorded using only the sensor 116 .
- a pulse 122 was measured to have a FWHM of about 21.6 keV.
- a spectrum 130 was also measured using the prior art relative gain compensation technique, which includes lowering the gain of the non-collecting grid below unity relative to that of the collecting grid.
- a peaking time of 2.4 ⁇ s was used.
- a full width half maximum (FWHM) of a pulse 132 centered at an energy of 662 keV corresponding to the 137 Cs was measured to be approximately 16.3 keV, with a contribution from the electronics of about 9.4 keV. With the sensor 116 unbiased, this contribution is about 6.9 keV.
- results from measurements using the ASIC 80 and compensation techniques based on the cathode/difference ratio are shown, where the measured spectrum 140 of the same 137 Cs standard shows a pulse 142 with FWHM of about 15 keV, a significant improvement in resolution.
- FIG. 8 also shows a spectrum 150 measured using the ASIC 80 .
- the first timing signal 112 and the second timing signal 114 are used to measure the timing difference t d ⁇ t c corresponding to the depth of interaction, according to the method of the present invention.
- a simple linear equation was applied for the compensation.
- the measured pulse 152 after the simple linear compensation was also measured to have a FWHM of about 15 keV, without the need for the high voltage bulky front-end electronics that are required to use a cathode input for the method applied to produce the pulse 142 in FIG. 7 .
- higher order equations are used as known to those skilled in the art to produce even better compensation.
- a bi-parametric spectrum 160 was measured relating the timing difference t d ⁇ t c 49 (see also FIG. 3A ) to the uncompensated amplitude of the shaped difference signal.
- the timing difference 49 is the difference between the timing signal 112 measuring time of occurrence t c 22 and timing signal 114 measuring time of detection t d 24 derived from the ASIC 80 .
- the corresponding depth of interaction is successfully used to compensate for the electron trapping according to the method and device of the present invention at a resolution comparable to or better than the less efficient prior art devices.
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Abstract
Description
d=a(t d −t c), (1)
where a is a weighting coefficient. Weighting of the difference signal to provide pulse height deficit correction is then performed, for example, by applying a linear equation for the compensation, such as:
E corr =E meas(1+b*d), (2)
where b is a second weighting coefficient, Emeas is the measured difference signal, and Ecorr is the resulting corrected difference signal obtained by weighting by the measured depth of interaction obtained from the present invention. Higher order equations may also be applied for the weighting operation according to means well-known to those skilled in the art. It is also possible to provide pulse height deficit correction that is an arbitrary function of the measured depth of interaction by doing a non-linear correction. Methods for providing correction to the difference signal are well-known to those skilled in the art and are discussed, for example, in: M. Amman, et al., “Optimization Criteria for Coplanar-Grid Detectors,” IEEE Trans. Nuc. Sci., Vol. 46, No. 3 (June 1999), last paragraph in Section II; Z. He, et al., “1-D Position Sensitive Single Carrier Semiconductor Detectors,” Nucl. Instr. and Meth. in Phys. Res. A, 380:228-231 (1996),
Claims (25)
d=a(t d −t c),
E corr =E meas(1+b*d),
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